Trace
The following is immediate:
Theorem. Suppose K is a continuous symmetric non-negative definite kernel; TK has a sequence of nonnegative eigenvalues {λi}i. Then
This shows that the operator TK is a trace class operator and
Read more about this topic: Mercer's Theorem
Famous quotes containing the word trace:
“To love someone is to isolate him from the world, wipe out every trace of him, dispossess him of his shadow, drag him into a murderous future. It is to circle around the other like a dead star and absorb him into a black light.”
—Jean Baudrillard (b. 1929)
“No trace of slavery ought to mix with the studies of the freeborn man.... No study, pursued under compulsion, remains rooted in the memory.”
—Plato (c. 427–347 B.C.)
“Beauty is a precious trace that eternity causes to appear to us and that it takes away from us. A manifestation of eternity, and a sign of death as well.”
—Eugène Ionesco (b. 1912)